# Lagrangian mechanics for a varible mass

Is it possible to find a lagrangian for a system with a varible mass and have a vaild solution when you are complete?

For instance, if I have a chain falling over the edge of a table or a rocket how would one approach this.

Example of my thinking:
For a chain falling over a table, if we assume that a sufficent portion of the entire mass is hanging over the edge (M'), than the lagrange will be something along the lines of:

L=1/2 (dm/dq)*v(t)^2 + M'gl; where q is a generalized coordinate, and l is how high the object is above the ground-level.

Anyone see anything wrong with this picture? Any other examples?

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I would think, since the derivation of Lagrange's equation is predicated on constant mass, that you would have to go back to the beginning and re-derive the results for variable mass. In fact, that might be an interesting exercise until itself...

I guess we could attempt to derive it from D'Alembert's principle, but that is just a guess.

I looked up some references. This one uses a Lagrangian in a slightly different context

httP://personnel.physics.ucla.edu/directory/faculty/fac_files/wong_cw/ajp_2006_falling_chains.pdf[/URL] [Broken]

And Dr Math seems to have solved it here -
http://mathforum.org/library/drmath/view/56302.html

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